This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384652 #11 Jun 06 2025 08:35:45
%S A384652 1,1,0,1,1,0,1,2,2,0,1,3,5,8,0,1,4,9,20,44,0,1,5,14,37,108,298,0,1,6,
%T A384652 20,60,198,716,2359,0,1,7,27,90,321,1290,5554,21112,0,1,8,35,128,485,
%U A384652 2064,9821,48838,209175,0,1,9,44,175,699,3091,15452,84888,476714,2262121,0
%N A384652 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A384145.
%F A384652 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(3*n-2*j+k,j)/(3*n-2*j+k) * A(n-j,j).
%e A384652 Square array begins:
%e A384652 1, 1, 1, 1, 1, 1, 1, ...
%e A384652 0, 1, 2, 3, 4, 5, 6, ...
%e A384652 0, 2, 5, 9, 14, 20, 27, ...
%e A384652 0, 8, 20, 37, 60, 90, 128, ...
%e A384652 0, 44, 108, 198, 321, 485, 699, ...
%e A384652 0, 298, 716, 1290, 2064, 3091, 4434, ...
%e A384652 0, 2359, 5554, 9821, 15452, 22805, 32315, ...
%o A384652 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-2*j+k, j)/(3*n-2*j+k)*a(n-j, j)));
%Y A384652 Columns k=0..1 give A000007, A384145.
%Y A384652 Cf. A379598, A384651, A384653, A384654.
%K A384652 nonn,tabl
%O A384652 0,8
%A A384652 _Seiichi Manyama_, Jun 06 2025